4125=n^2+20n+1200

Solution for 4125=n^2+20n+1200 equation:

Simplifying
4125 = n2 + 20n + 1200

Reorder the terms:
4125 = 1200 + 20n + n2

Solving
4125 = 1200 + 20n + n2

Solving for variable 'n'.

Combine like terms: 4125 + -1200 = 2925
2925 + -20n + -1n2 = 1200 + 20n + n2 + -1200 + -20n + -1n2

Reorder the terms:
2925 + -20n + -1n2 = 1200 + -1200 + 20n + -20n + n2 + -1n2

Combine like terms: 1200 + -1200 = 0
2925 + -20n + -1n2 = 0 + 20n + -20n + n2 + -1n2
2925 + -20n + -1n2 = 20n + -20n + n2 + -1n2

Combine like terms: 20n + -20n = 0
2925 + -20n + -1n2 = 0 + n2 + -1n2
2925 + -20n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
2925 + -20n + -1n2 = 0

Factor a trinomial.
(45 + -1n)(65 + n) = 0

Subproblem 1
Set the factor '(45 + -1n)' equal to zero and attempt to solve:

Simplifying
45 + -1n = 0

Solving
45 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-45' to each side of the equation.
45 + -45 + -1n = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -1n = 0 + -45
-1n = 0 + -45

Combine like terms: 0 + -45 = -45
-1n = -45

Divide each side by '-1'.
n = 45

Simplifying
n = 45
Subproblem 2
Set the factor '(65 + n)' equal to zero and attempt to solve:

Simplifying
65 + n = 0

Solving
65 + n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-65' to each side of the equation.
65 + -65 + n = 0 + -65

Combine like terms: 65 + -65 = 0
0 + n = 0 + -65
n = 0 + -65

Combine like terms: 0 + -65 = -65
n = -65

Simplifying
n = -65
Solution
n = {45, -65}